Ohms Law and Resistance Virtual Lab

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Valencia College *

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Dec 6, 2023

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PHYSICS II LAB Ohm’s Law Lab Ohm’s Law When combining the variables of voltage, resistance and current, German physicists Georg Ohm developed the formula: where V is the voltage in volts, I is the current in amps, and R is the resistance in Ohms ( Ω ). If the resistance is constant over a range of voltage this law can be used to predict the behaviour of the material. Whether or not a material obeys Ohms law, its resistance can be described in terms of the resistivity ρ . Resistance and resistivity The component in the resistance which takes into account the nature of the material is the resistivity which is represented by the Greek letter ρ (rho). As you will see in this experiment, resistance is linearly proportional to the length of the conductor and inversely proportional to the cross-sectional area. We can write the resistance formula as , where ρ is the electrical resistivity, is the length of the conductor and is the cross-sectional area of the conductor. In this lab, you will use two simulations to complete the experiments. The two simulations are shown in the figures below. Simulation 1 Simulation 2 V = IR , R = ρ l A l A 1

PHYSICS II LAB Exercise 1 In lecture, we discussed how to determine if a material is Ohmic or nonohmic. Take some time and consider the table below that shows voltage and current data for two different electrical devices. Which of the devices obeys Ohms Law? Refer to the lecture for review of this subject. All graphs must be attached and submitted with this packet to receive full credit for the problem. You can make two graphs or you can plot both on one graph. Data Table 1 (Jewett, 2019) Voltage applied to device (V) Current in Device 1 (A) Current in Device 2 (A) 1.00 0.123 0.123 2.00 0.249 0.250 3.00 0.365 0.389 4.00 0.486 0.545 5.00 0.621 0.701 6.00 0.745 0.909 7.00 0.854 1.230 8.00 0.984 1.550 9.00 1.102 1.719 10.0 1.241 1.747 2

PHYSICS II LAB In the space provided below explain how you determined if the device obeyed Ohms Law. Exercise 2 Procedure: 1. Open the Ohms Law simulation with the following link https://phet.colorado.edu/sims/html/ ohms-law/latest/ohms-law_en.html 2. Move the resistance slider to about 406 V. You will keep the voltage set at this value. Do not move the slider again for this part of the experiment. 3. Move the slider to 0.5 V. 4. Record the current in mA in the Data Table 2 below. 5. Repeat the process in increments of 0.5 V making sure you record the current for each increment. Analysis of data 6. Use Excel or Vernier Graphical Analysis to plot your data. Plot current on the Y axis and plot Voltage on the x-axis. 7. The slope of your graph is 1/R. What type of relationship is given by the graph? • The relationship given by the graph is a linear relationship. 8. What is the resistance? • Shown from the equation of the graph; 2.46*x + 5.88E-03, the slope of the graph would be 2.4. As mentioned above, slope = 1/R, therefore R=1/slope; R=1/2.4 = 0.41. The resistance is then to be calculated as 0.4 Ω . From the equation we can conclude that current is directly proportional to voltage with resistance being constant as V=IR. Based on the data from the table it is evident that as the voltage increases, the current within both devices also increase either at a specific rate or at different times. Taking all the data within the table and representing it visually through a graph we can confirm that as the voltage increases so does the current within both devices. However, to confirm whether they both obey Ohms law, we have to look at the characteristic of the graphs line. Only the current in device 1 can be seen at a constant increase showcasing its resistance is also constant and creating a direct linear graph, while the current in device 2 curves at the end. This observation can have us conclude that the only device that obeys Ohms Law would be device 1. Voltage (V) Current (mA) 0.5 1.2 1.0 2.5 3

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PHYSICS II LAB Data Table 2 1.5 3.7 2.0 4.9 2.5 6.1 3.0 7.4 3.5 8.6 4.0 9.8 4.5 11.1 5.0 12.3 5.5 13.5 6.0 14.7 6.5 16.0 7.0 17.2 7.5 18.4 8.0 19.7 8.5 20.9 9.0 22.1 4

PHYSICS II LAB Exercise 3 Procedure: 1. Open the resistance in a wire simulation with the following link: https://phet.colorado.edu/en/simulation/resistance-in-a-wire 2. Move the resistivity knob to 0.50 Ω cm. 3. Move the area knob to 7.50 cm 2 . 4. Move the length to 2 cm and take the measurement of the resistance R. Record the results in table 3 below. 5. Repeat the step above, increasing the length by 2 cm each time until you have completed all the measurements through 20.00 cm. Data Table 3 6. Use Microsoft Excel or Vernier Graphical Analysis to plot a graph of Resistance vs. Length. 7. Record your slope. m= 0.067. 8. From the slope of the line, find the resistivity ρ . Length (cm) Resistance ( Ω ) 2.00 0.132 4.00 0.269 6.00 0.399 8.00 0.536 10.0 0.667 12.0 0.797 14.0 0.934 16.0 1.06 18.0 1.20 20.0 1.33 5

PHYSICS II LAB 9. Calculate the percentage error. Slope is given by the graph as m=0.067 Ω /cm. When looking at what the slope actually represents we find that slope is basically calculated and given by Resistance/Length. Looking at the equation given: , and rearrange is to find resistivity ρ I get: ρ = A R/l Using the variables given and the fact that we know slope =R/l we can calculate ρ with slope. A = 7.50 cm 2 R/l = slope (m) = 0.067 Ω /cm ρ = A R/l ρ = (7.50 cm 2 )(0.067 Ω /cm ) ρ = 0.50 Ω cm R = ρ l A The given value of resistivity for the simulation is ρ = 0.50 Ω cm. The calculated value we got using slope was: ρ = 0.50 Ω cm. To find the percentage error we would use the equation: %error = (Given value - Calculated value)/Given Value x 100 = (0.50-0.50)/0.50 x100 = 0% 6

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PHYSICS II LAB Exercise 4 Procedure: 1. Open the resistance in a wire simulation with the following link: https://phet.colorado.edu/en/simulation/resistance-in-a-wire 2. Move the resistivity knob to 0.50 Ω cm. 3. Move the length knob to 10.00 cm. 4. Move the area knob to 2 cm 2 and take the measurement of the resistance R. Record the results in table 4 below. 5. Repeat the step above, increasing the length by 2 cm 2 each time until you have completed all the measurements through 14.0 cm 2 . Data Table 4 6. Using Microsoft Excel, plot a graph of Resistance vs. Area, then find the slope. • The slope (m) of the graph given is; -0.152. What is the shape of this graph? • The shape of this graph is hyperbolic. 7. Using Microsoft Excel, plot a graph of Resistance vs. 1/A, then find the slope. m = 5.06. 8. From the slope of the line, find the resistivity of the wire ρ . Area (cm 2 ) Resistance ( Ω ) 1/A (cm -2 ) 2.00 2.53 1/2 = 0.5 4.00 1.25 1/4 = 0.25 6.00 0.836 1/6 = 0.167 8.00 0.624 1/8 = 0.125 10.00 0.501 1/10 = 0.1 12.00 0.419 1/12 = 0.083 14.00 0.357 1/14 = 0.071 7

PHYSICS II LAB 9. Calculate the percentage error of the resistivity. From the previous question, to find resistivity I used the equation: ρ = A R/l. Looking at how the slope is derived in the second graph, we can see that slope = Resistivity/Area. As ρ = A R/l, and knowing that the area used in the second graph is actually 1/A, the equation can change to ρ = (1/A)(R/l) ρ = (1/l) (R/A) Taking the variables that we know: l = 10cm R/A = slope (m) = 5.0 Ω /cm 2 ρ = (1/l)(R/A) ρ = (1/10cm) (5.0 Ω /cm 2 ) ρ = 0.5 Ω cm The given value of resistivity for the simulation is ρ = 0.50 Ω cm. The calculated value we got using slope was: ρ = 0.50 Ω cm. To find the percentage error we would use the equation: %error = (Given value - Calculated value)/Given Value x 100 = (0.50-0.5)/0.50 x100 = 0% 8

PHYSICS II LAB Upon completion of this assignment, you should have a total of six graphs . Exercise 1: You should have 2 graphs. You can plot them on the same graph or you can plot them separately for this exercise. Exercise 2: You should have one graph Current vs. Voltage Exercise 3: You should have one graph Resistance vs. Length Exercise 4: You should have two graphs. (1) Resistance vs. Area and (2) Resistance vs. 1/Area. Make sure you show ALL OF YOUR WORK !!!! Failure to do so will result in point deductions. References Jewett, R. A. (2019). Physics for Scientists and Engineers 10th Edition . Boston: Cengage. 9

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